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The slow build to restock a depleted bullpen began Thursday for the Mariners.

The team announced it had signed free-agent lefty Zac Rosscupto a one-year contract. He’ll serve as a lefty specialist, something the Mariners lacked for much of last season.

“When healthy, Zac has swing-and-miss stuff, which has translated at all levels.” M’s general manager Jerry Dipoto said. “We look forward to seeing what he can do with good health and real opportunity.”

Seattle’s 40-man roster has 38 players on it.

Rosscup, 30, appeared in 17 games for the Dodgers in 2018, striking out 20 batters while and walking only four in 11 1/3 innings. He allowed six earned runs for a 4.76 ERA. A native of Clackamas, Ore., Rosscup held left-handed hitters to a slash line of .143/.280/.429. In a 10-appearance stretch from Aug. 17 to Sept. 25, he struck out 14 batters in 7 1/3 scoreless innings while allowing only three hits and issuing two walks.

Rosscup started the 2018 season with the Rockies but was claimed off waivers by the Dodgers on July 11. He made three separate stints to the disabled list — March 29 to July 11 (blister on left middle finger), July 25 to Aug. 4 (left middle finger inflammation) and Aug. 20 to Sept. 1 (left calf strain).

Over parts of five MLB seasons, he’s made 88 appearances, posting a 3-2 record with a 5.21 ERA. In 65 2/3 innings, he’s struck out 87 batters. For his career, lefties have posted have posted a .143/.266/.275 slash line with a 2.42 strikeout to walk ratio in 129 plate appearances.

Ryan Divish: 206-464-2373 or rdivish@seattletimes.com; on Twitter: @RyanDivish. Ryan Divish covers the Mariners and offers his perspective all season. He gives his inside look at Major League Baseball and power rankings every Sunday.